Höllig, Klaus
Overview
Works:  46 works in 143 publications in 2 languages and 1,197 library holdings 

Roles:  Author, Other, Creator 
Classifications:  QA224, 511.42 
Publication Timeline
.
Most widely held works by
Klaus Höllig
Box splines by
Carl De Boor(
Book
)
13 editions published between 1993 and 2010 in English and Undetermined and held by 393 WorldCat member libraries worldwide
This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an uptodate bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasiinterpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms
13 editions published between 1993 and 2010 in English and Undetermined and held by 393 WorldCat member libraries worldwide
This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an uptodate bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasiinterpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms
Finite element methods with Bsplines by
Klaus Höllig(
Book
)
13 editions published between 2003 and 2012 in English and Undetermined and held by 216 WorldCat member libraries worldwide
Finite Element Methods with BSplines describes new weighted approximation techniques, combining the computational advantages of Bsplines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for Bsplines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples
13 editions published between 2003 and 2012 in English and Undetermined and held by 216 WorldCat member libraries worldwide
Finite Element Methods with BSplines describes new weighted approximation techniques, combining the computational advantages of Bsplines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for Bsplines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples
Approximation and modeling with Bsplines by
Klaus Höllig(
Book
)
7 editions published in 2013 in English and held by 84 WorldCat member libraries worldwide
Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of Bspline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems with solutions available for instructors, slides for use in lectures, and programs with demos. Audience: Approximation and Modeling with BSplines is appropriate as an advanced undergraduate or firstyear graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and computer science. Practitioners in these fields who are using Bsplines in numerical simulations, computeraided design, and visualization will also find the book useful in their work. Amazon.com
7 editions published in 2013 in English and held by 84 WorldCat member libraries worldwide
Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of Bspline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems with solutions available for instructors, slides for use in lectures, and programs with demos. Audience: Approximation and Modeling with BSplines is appropriate as an advanced undergraduate or firstyear graduate text for courses on splines or approximation and geometric modeling for students in mathematics, engineering, and computer science. Practitioners in these fields who are using Bsplines in numerical simulations, computeraided design, and visualization will also find the book useful in their work. Amazon.com
Grundlagen der Numerik by
Klaus Höllig(
Book
)
1 edition published in 1998 in German and held by 30 WorldCat member libraries worldwide
1 edition published in 1998 in German and held by 30 WorldCat member libraries worldwide
BSplineApproximation elliptischer Randwertprobleme mit unstetigen Koeffizienten by
Andreas Keller(
)
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
1 edition published in 2013 in German and held by 16 WorldCat member libraries worldwide
Error estimates for the webmethod by
Klaus Höllig(
Book
)
4 editions published in 2000 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2000 in English and held by 9 WorldCat member libraries worldwide
Multivariate splines by
Klaus Höllig(
Book
)
6 editions published between 1981 and 1987 in English and Undetermined and held by 8 WorldCat member libraries worldwide
We prove recurrence relations for a general class of multivariate Bsplines, obtained as 'projections' of convex polyhedra. Our results are simple consequences of Stokes' theorem and include, as special cases, the recurrence relations for the standard multivariate simplicial Bspline. (Author)
6 editions published between 1981 and 1987 in English and Undetermined and held by 8 WorldCat member libraries worldwide
We prove recurrence relations for a general class of multivariate Bsplines, obtained as 'projections' of convex polyhedra. Our results are simple consequences of Stokes' theorem and include, as special cases, the recurrence relations for the standard multivariate simplicial Bspline. (Author)
$C \infty$regularity for the porous medium equation by
Klaus Höllig(
Book
)
8 editions published between 1984 and 1985 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords: estimates, approximation(mathematics); finite difference theory; finite element analysis
8 editions published between 1984 and 1985 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The equation stated in the abstract describes the expansion of a gas in a one dimensional porous medium. While existence of weak solutions can be obtained by standard energy methods, not much was known about regularity of the solution near the free boundaries. The difficulty is that the equation degenerates at the boundary and the hyperbolic term becomes dominant. The authors show in this report that despite of the degeneracy the free boundary is smooth with the possible exception of a discontinuity in the derivative at the waiting time. Their method is based on energy estimates in weighted norms using some of the ideas in another document. Additional keywords: estimates, approximation(mathematics); finite difference theory; finite element analysis
Nonuniform WEBsplines by
Klaus Höllig(
Book
)
3 editions published in 2002 in English and held by 8 WorldCat member libraries worldwide
3 editions published in 2002 in English and held by 8 WorldCat member libraries worldwide
Nonuniform WEBSplines by
Klaus Höllig(
)
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
Bsplines without divided differences by
Carl De Boor(
Book
)
8 editions published in 1985 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This note develops the basic Bspline theory without using divided differences. Instead, the starting point is the definition of Bsplines via recurrence relations. This approach yields very simple derivations of basic properties of spline functions and algorithms
8 editions published in 1985 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This note develops the basic Bspline theory without using divided differences. Instead, the starting point is the definition of Bsplines via recurrence relations. This approach yields very simple derivations of basic properties of spline functions and algorithms
Mehrfeldprobleme in der Kontinuumsmechanik = Geometric hermite interpolation with maximal order and smoothness by
Klaus Höllig(
Book
)
1 edition published in 1996 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 7 WorldCat member libraries worldwide
Divided differences, hyperbolic equations and lifting distributions by
Klaus Höllig(
Book
)
4 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
Convergence of cardinal series by
Mathematics Research Center (United States. Army)(
Book
)
5 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
5 editions published in 1985 in English and held by 6 WorldCat member libraries worldwide
The result of this paper is a generalization of an characterization of the limits of multivariate cardinal splines. Keywords: Convergence; fourier transforms; Analytic functions; Convolution; Exponential functions; Fourier series
Approximationszahlen von SobolevEinbettungen by
Klaus Höllig(
Book
)
3 editions published in 1979 in German and held by 5 WorldCat member libraries worldwide
3 editions published in 1979 in German and held by 5 WorldCat member libraries worldwide
Geometric hermite interpolation with maximal order and smoothness by
Klaus Höllig(
Book
)
2 editions published between 1995 and 1996 in English and held by 5 WorldCat member libraries worldwide
2 editions published between 1995 and 1996 in English and held by 5 WorldCat member libraries worldwide
Boxspline tilings by
Carl De Boor(
Book
)
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Geometric continuity of spline curves and surfaces by
Klaus Höllig(
Book
)
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
Box splines by
Klaus Höllig(
Book
)
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1986 in English and held by 4 WorldCat member libraries worldwide
A nonlinear integral equation occurring in a singular free boundary problem by
Klaus Höllig(
Book
)
3 editions published between 1983 and 1984 in English and held by 3 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
3 editions published between 1983 and 1984 in English and held by 3 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
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Related Identities
 Riemenschneider, S. D. Creator
 De Boor, Carl Author
 Society for Industrial and Applied Mathematics Publisher
 Hörner, Jörg
 Boor, Carl Author
 De Boor, Carl Author
 Reif, Ulrich
 Keller, Andreas Author
 Mathematics Research Center (United States. Army)
 Nohel, John A.
Associated Subjects
Algorithms Approximation theory Cauchy problemNumerical solutions Computer scienceMathematics Differential equations, Hyperbolic EngineeringMathematical models Finite element method Fourier series Global analysis (Mathematics) Interpolation Mathematical models Mathematics Multivariate analysis Numerical analysis Splines Spline theory Structural analysis (Engineering) Surfaces Tiling (Mathematics)